4 challenging SAT Math questions...

Test Preparation SAT Preparation
1

<p>Can someone please explain these SAT Math problems from the Blue Book (practice test #2)? Thanks! and here they are:</p>

<ol>
<li><p>The square of x is equal to 4 times the square of y. If x is 1 more than twice y, what is the value of x?
(a) -4
(b) -1/2
(c) -1/4
(d) 1/4
(e) 1/2</p></li>
<li><p>In the xy-coordinate plane, lines "l" and "q" are perpendicular. If line "l" contains the points (0,0) and (2,1), and line "q" contains the points (2,1) and (0,"t"), what is the value of "t"?
(a) -3
(b) -2
(c) 2
(d) 3
(e) 5</p></li>
</ol>

<p>And some open ended...
3. f(x)=|3x-17|
For the function defined above, what is one possible value of a for which f(a) < (a)?</p>

<ol>
<li><br>
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|<em>|</em>|<em>|</em>
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</ol>

<p>(^ That is supposed to be boxes stacked on top of each other, the bottom row has 4, the next highest 3, next 2, and the top has 1)</p>

<p>The figure above shows an arrangement of 10 squares, each with side of length "k" inches. The perimeter of the figure is "p" inches. The area of the figure is "a" square inches. If "p"="a", what is the value of "k"?</p>

<p>Much appreciated! (and I already have the answers if you need them posted)</p>

2

<p>1.
x^2 = 4 y^2
x = 2y+1</p>

<p>(2y+1) ^2 = 4 y^2 (substitution)
4y^2 + 4y + 1 = 4y^2
4y +1 = 0
4y = -1
y = -1/4
x = 2y+1
x = 2 (-1/4) +1 = -1/2 + 1 = 1/2
E.</p>

<p>2.</p>

<p>Perpendicular lines have negative reciprocal slopes.
l slope = (1-0) /(2-0) = 1/2
Therefore q slope must be -2
(t-1) / (0-2) = -2
(t-1) / -2 = -2
t -1 = 4
t = 5
E.</p>

<p>3.</p>

<p>if a = 5 then f(a) = 2
So 5 would work. For this just try to see where f(a) is small and make sure a is greater than it there.</p>

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<li>
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</ol>

<p>Perimeter = p = 16k (16 edges are there)
Area = a = 10 k^2
p=k, so
10k^2 = 16k</p>

<p>10k = 16
k = 16/10 = 8/5</p>

3

<p>Thank you OtherWindow!</p>

4

<p>Agree with every answer of OtherWindow… Good questions… GIMME MORE :P</p>

5

<p>Alright, I do have two more I’m a little confused about…</p>

<ol>
<li>[A picture of a typical right cylinder, with heigh h and diameter d]</li>
</ol>

<p>The right circular cylinder above has diameter d and heigh h. Of the following expressions, which represents the volume of the smallest rectangular box that completely contains the cylinder?
(a) dh
(b) d^2h
(c) dh^2
(d) d^2h^2
(e) (d+h)^2</p>

<p>This one I could get through guess + check, but I’m sure there’s a faster way? Here it is:
2.On a square gameboard that is divided into n rows of n squares each, k of these squares lie along the boundary of the gameboard. Which of the following is a possible value for k?
(a) 10
(b) 25
(c) 34
(d) 42
(e) 52</p>

6

<p>The smallest rectangular box that will fit the cylinder will be one that has a square base that is the length of the diameter and the height will be the height of the cylinder thus d^2h. Draw it out if you want.</p>

<p>When you draw out any of the game boards the number of squares on the boundary will be k=4n -4 only e will be an integer and so it will be the answer.</p>